Table 28-1 compares some values of x, some values of the first function, and some values of the
second function. The left-hand column contains selected values of x. The middle column contains
values of the linear function that we get when we input the chosen values of x. The right-hand
column contains values of the quadratic function that we get for the indicated values of x.Are you confused?
Do you wonder why we chose the values in Table 28-1 as we did? The two solutions can be tabulated eas-
ily, so it makes sense to include them:(x,y)= (−2,−3)and(x,y)= (3, 7)These solutions are written down in boldface. When we graph the functions, the points corresponding to
these solutions will be the points where the graphs intersect.
The other points are chosen strategically. We want to find ordered pairs that lie in the vicinity of the
solutions. That means we should choose values of x that are somewhat less than −2, somewhere between
−2 and 3, and somewhat larger than 3. Then, when we plot the graphs, we can expect to get a good view
with the solutions near the middle. We calculate the values of the functions in the middle and right-hand
columns by plugging in the values of x and going through the arithmetic.Next, we plot the solution(s)
To plot the solutions of this system, we could use a strict Cartesian plane with each division
on both axes equal to 1 unit. But we must cover a span of −4 to 5 for the independent vari-
able, and a span of −7 to 25 for the dependent variable, based on the function values we have
found in Table 28-1. A true Cartesian graph having that span would be as big as a road map!464 More Two-by-Two Graphss
Table 28-1. Selected values for graphing the functions
y= 2 x+ 1 and y=x^2 +x− 5.
Bold entries indicate real solutions.
x 2 x+ 1 x^2 +x− 5
− 4 −7 7
− 3 −5 1
− 2 − 3 − 3
0 1 − 5
1 3 − 3
37 7
4 9 15
5 11 25